On the other hand, this reaction creates a SF bordered by the partial dislocations. The required SF energy limits the separation of the two partial dislocations.
An extension to the concept of the Thompson tetrahedron has to be made for the sphalerite structure which is the combination of two fcc lattices. The presence of double layers (Aβ, Bγ and Cα; see figure 2.1) provides two distinct positions of the dislocation lines on {111}
planes. The bonds within the double layer or between two double layers can be broken.
These two locations are referred to as glide and shuffle set, respectively.
Defects of all dimensionalities are encountered in chapter 4 and are described in more detail where necessary.
2.1.2. Heteroepitaxy of III-V semiconductors
The combination of different III-V materials as well as their integration in established silicon technology is faced to challenges which are traced back to the interfaces of the heterostruc-tures. The epitaxial deposition of layers (epilayers) on single crystalline substrates is con-sidered in the following. Provided that the interface is chemically stable and that a direct growth without intermediate layer is possible, the similarity of crystal symmetry, lattice con-stants and bonding character promotes the successful formation of a smooth heterostructure interface and a single crystalline layer. A mismatch of the structures entails the formation of defects like threading dislocations (TD) which can work, for instance, as path for leakage currents in opto-/electronic devices [64, 65]. The crystal structures and the lattice constants as presented in figures 2.1 and 2.2 are taken into account.
The impact of symmetry is regarded at first. The combination of cubic, covalent materials allows a one-to-one match of covalent bonds at the interface for equally oriented substrate and layer. This applies for III-V heterostructures as well as for the integration of III-V semiconductors on Si. A cube-on-cube growth can be realized in this case, i.e. (001)S k (001)Land [100]Sk[100]L(S and L denote the substrate and epilayer). The combination of the wurtzite structured III-V heterostructures with cubic materials fits symmetrically for the bonding of atoms on the hexagonal (0001) and the cubic (111) surfaces with the in-plane orientation [11¯20] k [1¯10]. The orientation relationship implies that the wurtzite lattice constantahas to be compared to the spacing of the {110} lattice planesd110=a/√
2in the cubic structures.
Si has an inversion centre in contrast to the sphalerite structure and, hence, it does not exhibit a polar axis. The heteroepitaxy of polar III-V materials on non-polar substrates is prone to the formation of inversion domains and anti-phase boundaries in the epilayer. This aspect is considered in sections 4.2.2 and 4.3.
On the other hand, the match of lattice constants has to be considered for the formation of an epitaxial interface. The realization of heterostructures with exactly the same lattice dimensions requires lattice constant engineering with ternary or quaternary alloys. In
gen-(a) (c)
substrate epilayer
aS aL
aS aL┴
aL║
(b)
Figure 2.4.Models for epitaxial interfaces (c) Semi-coherent interfaces and in large misfit heterostructures where lattice constant is commensurable (middle) or incommensurable (bottom).
eral, a mismatch between the substrate and the layer exists and the epitaxial film reacts to this difference. The initial situation is displayed in figure 2.4(a). An interface between two lattices with different lattice constants has to be established. The first case is depicted in figure 2.4(b). It occurs for materials with a small lattice mismatch. Promising combinations emerge from the comparison of semiconductors in figure 2.2(b). The semiconductors with the lattice constant around 6.1 Å are already mentioned above. GaP and AlP are predestined for the integration on Si. The schematic shows a coherent interface between the substrate and the compressively strained epilayer (aL>aS). In consequence, the layer becomes tetra-hedrally distorted, i.e. a⊥L >akL. This pseudomorphic growth works until a critical thickness is reached which depends on the lattice mismatchf and the elastic properties of the involved materials [66, 67].
f = aS−aL aS
(2.2) The exceeding of the critical thickness causes the introduction of misfit dislocations (MFD) into the layer. They nucleate at the surface and leave threading segments within the layer [68]. An attempt to suppress this route of TD formation is the introduction of a buffer layer. Either this layer exhibits a certain thickness to allow for the annihilation of defects by dislocation interactions or it is designed to as template to match the lattice constants of substrate and epilayer. For instance, the lattice constants of Si and GaAs have been mediated by the application of a graded Si1-xGexbuffer layer [69]. Alternatively, the filtering of TDs by strained layer superlattices or the post growth treatment by thermal cycling has been considered (see, e.g. [70]).
The integration of highly mismatched systems is also feasible by the formation of a coin-cidence site lattice which is depicted in figure 2.4(c) [71]. The upper image illustrates the existence of lattice planes (red lines) that are in register before the contact of substrate and layer is established. If the quotient of the lattice constants
aS aL = m
n m, n∈N (2.3)
is representable by m and n, a coincidence site lattice (CSL) can be formed. The crystal lattices are commensurable. The CSL period is m·aL = n·aS. The middle image shows
the merged crystals with a semi-coherent interface. A MFD is introduced within each period of the CSL, i.e. a periodic MFD network is created. The spacing of MFDssis expressed by equation 2.3 or by means off and the Burgers vector
s=~bk
f . (2.4)
~bk is the Burgers vector component parallel to the interface plane and perpendicular to the MFD line direction. Usually, the situation is less ideal and the lattices are incommensurable.
mandnonly approximate the lattice constant quotient. One solution is the occasional alter-nation of the coincidence distance realized bym+ 1andn+ 1lattice planes [72]. Otherwise there remains residual stress which is considered in section 4.3.2.1. Beyond, the CSL idea extends the possibilities to combine materials with different symmetries of adjoining lattice planes (see, for instance, [73]). The formation mechanism of a MFD network is discussed in section 4.2. The dislocations at the heterostructure interfaces are treated with respect to the Thompson tetrahedron. This simplification ignores the dissimilar materials because the Burgers vector is defined with reference to the ideal bulk lattice. A correct description would require the model of grain boundary dislocations [74].
The eventually formed interfaces sketched in figure 2.4 are tacitly established at a fixed temperature. A mismatch in thermal expansion coefficients introduces a lattice mismatch during the sample cooling after growth. Additionally required MFDs have to nucleate at the surface and move toward the interface. An estimate of the thermally induced strain is given in section 4.3.2.1 for the epitaxy of GaSb on Si(001).
Beside the 2D growth mode, there are material combinations and growth regimes where 3D structures establish on the substrate surface instead of closed layers. Considering the free surface energy of the substrateγS, the layerγLand the free energy of the interface γI, the following inequations characterize the 3D (Volmer-Weber) and the 2D layer-by-layer (Frank-van-der-Merwe) growth mechanism, respectively [69].
γS < γL+γI (2.5)
γS > γL+γI (2.6)
The 3D growth regime is exploited, amongst other things, in order to circumvent the forma-tion of threading dislocaforma-tions. The 3D objects exhibit a free surface which allows to expand the lattice and reduce the epitaxially and thermally imposed strain [75]. Furthermore, the dislocations tend to be as short as possible in order to minimize the energy according to their length. The 3D object provides more options for a dislocation to terminate at a surface. Two competing approaches toward 3D structures, namely nanowires, have been considered. The self-organized growth where inequation 2.5 is valid, and the growth through the holes in a mask on a prepatterned substrate [75].
In the presented work, two heteroepitaxial material systems are considered as case studies.
They are described in appendix A. One system corresponds to a large misfit system that forms a MFD network. The other one is an example for the selected area growth (SAG), i.e.
the 3D growth by the application of a mask.